We studied the properties of the neutral gas in a sample of 38 local luminous and ultra luminous infrared galaxies ( [ U ] LIRGs , 51 individual galaxies at z \leq 0.09 ) , which mainly covers the less explored LIRG luminosity range . This study is based on the analysis of the spatially integrated and spatially resolved spectra of the NaD \lambda \lambda 5890,5896 \AA feature obtained with the integral field unit ( IFU ) of VIMOS at the Very Large Telescope . Analyzing spatially integrated spectra , we find that the contribution of the stars to the observed NaD equivalent width is small ( < 35 \% ) for about half of the sample , and therefore this feature is dominated by inter stellar medium ( ISM ) absorption . After subtracting the stellar contribution , we find that the pure-ISM integrated spectra generally show blueshifted NaD profiles , indicating neutral gas outflow velocities , V , in the range 65-260 kms ^ { -1 } . Excluding the galaxies with powerful AGNs , V shows a dependency with the star formation rate ( SFR ) of the type V \propto SFR ^ { 0.15 } , which is in rather good agreement with previous results . The spatially resolved analysis could be performed for 40 galaxies , 22 of which have neutral gas velocity fields dominated by noncircular motions with signatures of cone-like winds . However , a large number of targets ( 11/40 ) show disk rotation signatures . Based on a simple model , we found that the wind masses are in the range 0.4 - 7.5 \times 10 ^ { 8 } M _ { \sun } , reaching up to \sim 3 \% of the dynamical mass of the host . The mass rates are typically only \sim 0.2-0.4 times the corresponding global SFR indicating that , in general , the mass loss is too small to slow down the star formation significantly . In the majority of cases , the velocity of the outflowing gas is not sufficient to escape the host potential well and , therefore , most of the gas rains back into the galaxy disk . On average V/v _ { esc } is higher in less massive galaxies , confirming that the galaxy mass has a primary role in shaping the recycling of gas and metals . The comparison between the wind power and kinetic power of the starburst associated with SNe indicates that only the starburst could drive the outflows in nearly all the [ U ] LIRGs galaxies , as the wind power is generally lower than 20 \% of the kinetic power supplied by the starburst . The contribution of an active galactic nuclei ( AGN ) is , in principle , significant in two cases .